Why do this problem?
Use this activity
to introduce the youngsters to an investigation that mixes both shape and space work with number work. You could also introduce learners to this extended piece of work to help you look at perseverence and persistence.
A good introduction can be had with the whole class by making the first two or three arrangements all together. It is useful to have squared and dotted (squares) paper available whilst some pupils may benefit from using blocks (such as multilink) to represent the pebbles. You may also find it helpful to use a virtual geoboard
for sharing ideas amongst the whole
After children have worked in pairs for a time, investigating subsequent arrangements, you can pose some of the suggested questions (for example looking at the number of pebbles added each time) and invite them to ask and explore their own questions. Encourage record keeping in whatever form the pupils feel is appropriate.
What are you counting? (Sometimes there is confusion about the counting of the pebbles and the counting of the spaces in between them - particularly along the lengths of sides.)
Is this rectangle double the size of the last one?
How are you recording what you have done?
Some pupils may produce a table or a spreadsheet of their results which would enable them to explore further.
Here is an example of many results that lead to the consideration of the digital roots (d.r.):
Alternatively, Making Squares
is an extension activity.
For more extension work
Children may benefit from adult support in keeping track of where they are in their exploration. They could be helped to proceed as if it were a game.